r^2+9r-110=0

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Solution for r^2+9r-110=0 equation: 


Simplifying
r2 + 9r + -110 = 0

Reorder the terms:
-110 + 9r + r2 = 0

Solving
-110 + 9r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '110' to each side of the equation.
-110 + 9r + 110 + r2 = 0 + 110

Reorder the terms:
-110 + 110 + 9r + r2 = 0 + 110

Combine like terms: -110 + 110 = 0
0 + 9r + r2 = 0 + 110
9r + r2 = 0 + 110

Combine like terms: 0 + 110 = 110
9r + r2 = 110

The r term is 9r.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9r + 20.25 + r2 = 110 + 20.25

Reorder the terms:
20.25 + 9r + r2 = 110 + 20.25

Combine like terms: 110 + 20.25 = 130.25
20.25 + 9r + r2 = 130.25

Factor a perfect square on the left side:
(r + 4.5)(r + 4.5) = 130.25

Calculate the square root of the right side: 11.412712211

Break this problem into two subproblems by setting 
(r + 4.5) equal to 11.412712211 and -11.412712211.


Subproblem 1
r + 4.5 = 11.412712211

Simplifying
r + 4.5 = 11.412712211

Reorder the terms:
4.5 + r = 11.412712211

Solving
4.5 + r = 11.412712211

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-4.5' to each side of the equation.
4.5 + -4.5 + r = 11.412712211 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + r = 11.412712211 + -4.5
r = 11.412712211 + -4.5

Combine like terms: 11.412712211 + -4.5 = 6.912712211
r = 6.912712211

Simplifying
r = 6.912712211


Subproblem 2
r + 4.5 = -11.412712211

Simplifying
r + 4.5 = -11.412712211

Reorder the terms:
4.5 + r = -11.412712211

Solving
4.5 + r = -11.412712211

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-4.5' to each side of the equation.
4.5 + -4.5 + r = -11.412712211 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + r = -11.412712211 + -4.5
r = -11.412712211 + -4.5

Combine like terms: -11.412712211 + -4.5 = -15.912712211
r = -15.912712211

Simplifying
r = -15.912712211


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.912712211, -15.912712211}

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